Square lattice
2-dimensional integer lattice / From Wikipedia, the free encyclopedia
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In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space. It is the two-dimensional version of the integer lattice, denoted as .[1] It is one of the five types of two-dimensional lattices as classified by their symmetry groups;[2] its symmetry group in IUC notation as p4m,[3] Coxeter notation as [4,4],[4] and orbifold notation as *442.[5]
Two orientations of an image of the lattice are by far the most common. They can conveniently be referred to as the upright square lattice and diagonal square lattice; the latter is also called the centered square lattice.[6] They differ by an angle of 45°. This is related to the fact that a square lattice can be partitioned into two square sub-lattices, as is evident in the colouring of a checkerboard.